Bowden Belt and Pinion

Builder

Let's say I have GT2 belt mounted inside an extrusion and a carriage. But because I need the carriage to be light, I can't mount a motor onto it. So I mount the motor at the end of the extrusion. Remember, the belt doesn't move.

Theoretically, is there a power transmission system that can transfer rotation to the carriage despite the fact it will move and its distance from the motor will increase and decrease?